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\begin{document}
\setcounter{page}{16}

\noindent\parbox{2.85cm}{\includegraphics*[keepaspectratio=true,scale=1.75]{BJMA.jpg}}
\noindent\parbox{4.85in}{\hspace{0.1mm}\\[1.5cm]\noindent
Banach J. Math. Anal. 3 (2009), no. 2, 16--27\\
$\frac{\rule{4.55in}{0.05in}}{{}}$\\
{\footnotesize
\textcolor[rgb]{0.65,0.00,0.95}{\textsc{\textbf{\large{B}}anach
\textbf{\large{J}}ournal of \textbf{\large{M}}athematical
\textbf{\large{A}}nalysis}}\\
ISSN: 1735-8787 (electronic)\\
\textcolor[rgb]{0.00,0.00,0.84}{\textbf{http://www.math-analysis.org }}\\
$\frac{{}}{\rule{4.55in}{0.05in}}$}\\[.5in]}

\title[$E_0$--Semigroups for Product Systems: The Nonunital Case]{$E_0$--Semigroups for Continuous Product Systems:\\The Nonunital Case}

\author[M.\ Skeide]{Michael Skeide}

\address{Universit\`a\ degli Studi del Molise, Dipartimento S.E.G.e S., Via de Sanctis, 86100 Campobasso, Italy.}

\email{\textcolor[rgb]{0.00,0.00,0.84}{skeide@unimol.it}}

\dedicatory{{\rm Communicated by M. Frank}}

\subjclass[2000]{Primary 46L55; Secondary 46L53, 46L08.}

\keywords{Quantum probability, quantum dynamic, product system,
Hilbert module, classification.}

\date{Received: 13 January 2009; Accepted: 7 April 2009.}

\begin{abstract}
Let $\cB$ be a \nbd{\sigma}unital \nbd{C^*}algebra. We show that
every strongly continuous \nbd{E_0}semigroup on the algebra of
adjointable operators on a full Hilbert \nbd{\cB}module $E$ gives
rise to a full continuous product system of correspondences over
$\cB$. We show that every full continuous product system of
correspondences over $\cB$ arises in that way. If the product system
is countably generated, then $E$ can be chosen countably generated,
and if $E$ is countably generated, then so is the product system. We
show that under these countability hypotheses there is a one-to-one
correspondence between \nbd{E_0}semigroups up to stable cocycle
conjugacy and continuous product systems up to isomorphism. This
generalizes the results for unital $\cB$ to the \nbd{\sigma}unital
case.
\end{abstract} \maketitle
\vspace{1in}

\end{document}

.
